Since you don't have any links to logs, here's my two cents on what you can do.
-Having done the fight multiple times as affliction, destro, and demo, I find that destro and demo generally pulled better numbers overall, with less effort. As Affliction, you need to time your aoe perfectly in order to keep up with other classes.
- As for being under hit cap, it's you're own personal choice. On progression fights, I run hit cap if I am affliction (rare on heroics), and once we have a kill, I run less hit.
- If you choose to stay affliction, make sure to refresh your shards on any diffusion chain adds, and ball lightning adds. This will up your dps a fair bit.

The balls are a huge factor in terms of staying with the other dps, affliction just doesn't have the instant aoe that Demo and Destruction have so by the time you've got 1 or 2 Seeds off (if your raid is hugging for the balls) then they will die before you get any meaningful aoe out.

Originally Posted by Crym

Spoiler: The reason Garrosh is defeated is because, just when he's being attacked, Malchezaar pops out of a portal, yells "yoink!", and takes his weapon away.

Destro is probably the better choice. FnB along with MF is an absolute ball lightning wrecker and you'll outdps everyone on the balls if they're not gripped and stunlocked.

Slightly off-topic, you should really really go for that helm socket bonus. If you're worried about the haste breakpoint, put a 320 haste gem in that yellow leg slot and a haste + hit gem in your helm.

Is your raid struggling on ball lightning DPS? Are you wiping because of that?
- If yes then you will be better of using a destro or demono spec.
- If no then, are you competitive DPS wise on Lei Shen alone?

Is your raid gripping and stunning the ball lighting?
- If yes, a KJC build for destro/demono might allow you to pull some great numbers (keep two chaos wave ready, wait for the grip, cast them, done).
- If no, this might be something your raid might want to do to improve the overall DPS (less damage on you, more cleave on the boss).

KJC will be very usefull for P3.
MF will be usefull if there is no grip/stun on the aoe phase.

You can push pretty competitive dps with affliction on LS, if you are struggling with your damage on the ball lightnings you need to focus on your timing and getting the spells of correctly. Your overall dps will mostly vary (if you play correctly otherwise) on the factor how many diffusion adds you get to dps during the transition phases, if your segment doesn't have to deal with any adds, it's normal that you encounter difficulties to upkeep your dps.
Also obviously your raid size is a factor, if you are running 10 mans, and struggling to kill the ball lightnings you should consider playing destruction, unless you have formidable experience playing demo.
Most important is that you compare the damage done to the boss, from world of logs, between players to get more realistic numbers on your performance, if you are noticeably lower on damage done to the boss, then you need to focus on improving your single target performance.

Affliction pulls good numbers on normal lei shen but with the way you gear flat haste in every socket you are gimping yourself. Idk who told you to ignore socket bonuses but that's an awful idea on every piece of gear except maybe the heroic iron qon ring. Put expertise/haste gems in red flat haste in yellow and haste hit in blues. Then you just need to reforge for UA or Agony thresholds with ur haste while staying hit capped and then dump the rest into mastery. Timing is everything on the ball lightning. You really don't need to go a different spec for the normal mode version of the fight because ball lightning and overall dps should not be an issue unless ur trying to carry 3 afk dps or something ridiculous. Once you get him down get a demo spec ready for when you get an unerring and you will be all set for heroics.

Affliction isn't terrible for the fight. While I have done the last 2 weeks as destro, I was affliction before that. I was able to keep up with the other locks, assuming I had near perfect timing on the aoe for ball lightning. It's by no means easy, and if you want an easier time, play destro.